If 31 elements are distributed equally into (amongst) zero groups... How is that not either 31 or 0????

Because the result of division is the number of elements within each one of the groups. We are counting the number of elements within groups, not the number of elements outside of these groups. When there are no groups, there is nothing to count, therefore, the result is undefined.

I got a philosophy degree, I'm not upset that I can't find work as a philosopher. It was my decision, and I knew that it wasn't a money making degree, so I get money elsewhere.-- Mr. Reasonable

If 31 elements are distributed equally into (amongst) zero groups... How is that not either 31 or 0????

Because the result of division is the number of elements within each one of the groups. We are counting the number of elements within groups, not the number of elements outside of these groups. When there are no groups, there is nothing to count, therefore, the result is undefined.

Ecmandu this is getting silly. Now everyone is telling you that you are wrong but you are not listening to them. You have to realise that maths is useless unless there is universal agreement on the function of its axioms and everyone here know this apart from you

I'm not a mathematician so bear with my inexperience... but I don't think that anybody here has actually stipulated which definition of "0" they are working with?

If 0 is understood as a Robinson infinitesimal in non-standard analysis, then 2/0 does indeed equal infinity, and 0/2 does indeed equal 0 (I think. I'm not pretending I understand non-standard analysis - I read about it in a book). On the other hand, if 0 is considered as "the null set", the expression 0/2 is simply not admissible because the null set does not contain 2 subsets. (In fact you might like to argue, just to be mischievous, that to be divisible by 2, the null set would have to contain three subsets - can you guess why?)

Mathematics is another language altogether, and what you expressed pretty well describes the philosophical underpinnings of the different meanings of 0. Mathematically, 0 deals with value in the abstract, whereas 0=nothingness deals with the substantial, philosophical underpinnings of meaning.

alan1000 wrote:I'm not a mathematician so bear with my inexperience... but I don't think that anybody here has actually stipulated which definition of "0" they are working with?

If 0 is understood as a Robinson infinitesimal in non-standard analysis, then 2/0 does indeed equal infinity,

That could be true except to refer to hyperreal numbers requires that one use hyperreal notation or at very least specify such. A variety of hyperreal notations have been offered by pretty well known mathematicians. I have my own notation (for philosophical reasons). And another thing that is required, although unknown to many mathematicians, is logic. Mathematics is a subset of logic and cannot defy logic in its construction without becoming incoherent and useless.

alan1000 wrote:and 0/2 does indeed equal 0 (I think. I'm not pretending I understand non-standard analysis - I read about it in a book).

Again, if using proper notation, "0" is undefined because the "degree of 0" isn't being specified. 0.000...:000 / 2 would still be 0.000...:000or my own notation:[0.000...:0R] / 2 = [0.000...:0R] {R == "eternally Remaining amount for sake of non-ending decimals"}.

alan1000 wrote:On the other hand, if 0 is considered as "the null set", the expression 0/2 is simply not admissible because the null set does not contain 2 subsets.

That is an excellent observation, although I would disagree with your logic.

One cannot divide 2 by a null set, because the statement itself makes no sense (hence is "undefined"). But dividing nothing yields nothing, always. The number of parts requested is irrelevant. Thus;0/2 = 0, just as standard analysis proposes.

alan1000 wrote:(In fact you might like to argue, just to be mischievous, that to be divisible by 2, the null set would have to contain three subsets - can you guess why?)

I am curious of your reasoning.

Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic HarmonyElseFrom THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.The only absolute certainty is formed by the absolute lack of alternatives.It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is"..

unlz wrote:it is indeed possible to divide with zero, to do so you must lose the math mindset and think of zero as a starting point.

How can you divide two apples into a "starting point"?

Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic HarmonyElseFrom THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.The only absolute certainty is formed by the absolute lack of alternatives.It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is"..

Infinity and undefined start being really important when you hit calculus. But it's not just that. Programming is hot. Trying to argue that X/0 is anything other than "undefined" will upend any programming language.

Absent theory where I'm not an expert (though I could talk to some), what practical gains would be made by a not-undefined answer?

Xunzian wrote:Absent theory where I'm not an expert (though I could talk to some), what practical gains would be made by a not-undefined answer?

Not having to handle all of those exceptions, would be nice.

Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic HarmonyElseFrom THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.The only absolute certainty is formed by the absolute lack of alternatives.It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is"..

That's an easy mistake to make. Especially if you only know enough to be dangerous.

But breaking a tool to make it useless to those that use it but approachable to those who don't seems like a really ass-backwards approach.

I'm not one of those trying to, nor wanting to, change it. I am the one trying to explain the sense in the original intent.

Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic HarmonyElseFrom THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.The only absolute certainty is formed by the absolute lack of alternatives.It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is"..

math is not pear and apples. to get somewhere in these things you need to think outside of the box. starting point is a abstract term in lack of better words for it. zero is holy grail of mathemathics but i feel only coz of a designer error where everything is this and that and cannot be anything else. its not. my intuiton tells me that zero is something you can see. like the thing that makes black holes or something like that..im tellin u, my intuition i rarely wrong.